Self-balancing mobile robots represent an important area of modern robotics, as they offer high maneuverability, compact size, and the ability to operate in confined spaces. Such systems are widely used in service robotics, transport systems, educational platforms, and autonomous mobile devices. The main challenge in the development of such robots lies in ensuring the stability of a dynamic system equivalent to an inverted pendulum, which is inherently unstable. This paper considers the development and study of a stabilization system for a two-wheeled self-balancing robot under changing external conditions, such as external disturbances and variations in platform mass. A control algorithm based on feedback from the tilt angle and angular velocity obtained from the MPU6050 inertial measurement unit is proposed. A complementary filter is used to process sensor data, providing fusion of gyroscope and accelerometer information and improving the accuracy of tilt angle estimation. To analyze the system dynamics, a mathematical model of the balancing robot was developed based on representing the system as an inverted pendulum on a cart. The model was transformed into state-space form, which made it possible to implement and investigate various control algorithms. Two types of controllers were implemented in this study: a classical PID controller and an optimal LQR controller. System simulation was carried out in the MATLAB/Simulink environment. Experimental studies included an analysis of the system response to various types of inputs, including impulse and step disturbances, as well as verification of stability under variations in robot mass. The obtained results showed that both control methods ensure system stability; however, the LQR controller demonstrates higher stabilization accuracy and smaller oscillations. The proposed stabilization algorithm can be used in the development of mobile robotic systems operating under uncertainty and changing external parameters.